A cam rotating clockwise with a uniform speed is to give the roller follower of 20 mm diameter with the following motion: (a) Follower to move outwards through a distance of 30 mm during 120° of cam rotation; (b) Follower to dwell for 60° of cam rotation; (c) Follower to return to its initial position during 90° of cam rotation; and (d) Follower to dwell for the remaining 90° of cam rotation. The minimum radius of the cam is 45 mm and the line of stroke of the follower is offset 15 mm from the axis of the cam and the displacement of the follower is to take place with simple harmonic motion on both the outward and return strokes. Draw the cam profile.